# Answer to Question #23763 in Linear Algebra for Matthew Lind

Question #23763

Prove that a square matrix is invertible if and only if it has a full rank.

Expert's answer

Let we have invertible n byn matrix A, then det A is nonzero. So, there is minor of size n, hence A has

full rank.

Conversely, if A has full rank then there is minor of size n, hence A has

nonzero det A, and we can explicitely compute A^-1, so A is invertible.

full rank.

Conversely, if A has full rank then there is minor of size n, hence A has

nonzero det A, and we can explicitely compute A^-1, so A is invertible.

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